Rational functions and modular forms

• Verfasst von: Franke, Johann [VerfasserIn]
• Titel: Rational functions and modular forms
• Verf.angabe: J. Franke
• E-Jahr: 2020
• Jahr: [October 2020]
• Umfang: 14 S.
• Fussnoten: Article electronically published on June 30, 2020 ; Gesehen am 18.09.2020
• Titel Quelle: Enthalten in: American Mathematical SocietyProceedings of the American Mathematical Society
• Ort Quelle: Providence, RI : Soc., 1950
• Jahr Quelle: 2020
• Band/Heft Quelle: 148(2020), 10, Seite 4151-4164
• ISSN Quelle: 1088-6826
• DOI: doi:10.1090/proc/15034
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: contour integration
• Sach-SW: Eisenstein series
• Sach-SW: rational functions
• Sach-SW: Weil’s converse theorem
• K10plus-PPN: 1733331298

Abstract

There are two elementary methods for constructing modular forms that dominate in literature. One of them uses automorphic Poincaré series and the other one theta functions. We start a third elementary approach to modular forms using rational functions that have certain properties regarding pole distribution and growth. We prove modularity with contour integration methods and Weil's converse theorem, without using the classical formalism of Eisenstein series and -functions.